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The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…

Statistical Mechanics · Physics 2009-10-30 M. Krech

We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has…

High Energy Physics - Theory · Physics 2016-08-02 Ali Hosseiny , Shahin Rouhani

We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…

Statistical Mechanics · Physics 2026-03-04 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

We prove here that the height function associated to non-simple exclusion processes with arbitrary jump-length converges to the solution of the Kardar-Parisi-Zhang SPDE under suitable scaling and renormalization. This extends the work of…

Probability · Mathematics 2022-12-23 Kevin Yang

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…

Statistical Mechanics · Physics 2012-06-25 Kazumasa A. Takeuchi , Masaki Sano

The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces.…

Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…

Soft Condensed Matter · Physics 2007-05-23 S. V. Ghaisas

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Statistical Mechanics · Physics 2009-11-07 Anna Chame , Fabio D. A. Aarao Reis

Ballistic deposition (BD) is considered to be a paradigmatic discrete growth model that represents the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we question this connection by rigorously deriving a formal continuum…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

Using the weak-noise theory, we evaluate the probability distribution $\mathcal{P}(H,t)$ of large deviations of height $H$ of the evolving surface height $h(x,t)$ in the Kardar-Parisi-Zhang (KPZ) equation in one dimension when starting from…

Statistical Mechanics · Physics 2016-02-23 Baruch Meerson , Eytan Katzav , Arkady Vilenkin

To investigate universal behavior and effects of long-range temporal correlations in kinetic roughening, we perform extensive simulations on the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise based on pseudospectral…

Statistical Mechanics · Physics 2023-04-18 Xiongpeng Hu , Dapeng Hao , Hui Xia

Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative…

Statistical Mechanics · Physics 2024-01-29 Andrea Cavagna , Javier Cristín , Irene Giardina , Mario Veca

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…

Statistical Mechanics · Physics 2013-04-01 Amit K. Chattopadhyay

The $(d+1)$-dimensional KPZ equation is the canonical model for the growth of rough $d$-dimensional random surfaces. A deep mathematical understanding of the KPZ equation for $d=1$ has been achieved in recent years, and the case $d\ge 3$…

Probability · Mathematics 2019-05-30 Sourav Chatterjee , Alexander Dunlap

A comprehensive theory of the Kosterlitz-Thouless transition in two-dimensional superfluids in thermal equilibrium can be developed within a dual representation which maps vortices in the superfluid to charges in a Coulomb gas. In this…

Statistical Mechanics · Physics 2016-09-29 L. M. Sieberer , G. Wachtel , E. Altman , S. Diehl

We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle…

Probability · Mathematics 2024-12-11 Kevin Yang

We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the…

Statistical Mechanics · Physics 2012-06-15 Takashi Imamura , Tomohiro Sasamoto

Control of generically scale-invariant systems, i.e., targeting specific cooperative features in non-linear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized…

Statistical Mechanics · Physics 2020-02-05 Priyanka , Uwe C. Täuber , Michel Pleimling

We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal…

Statistical Mechanics · Physics 2025-08-04 Romain Daviet , Carl Philipp Zelle , Armin Asadollahi , Sebastian Diehl

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…

Statistical Mechanics · Physics 2009-11-10 Francesco Ginelli , Haye Hinrichsen